Analytical Models for the Energetics of Cosmic Accretion Shocks, their Cosmological Evolution, and the Effect of Environment

We present an analytical description of the energetics of the population of cosmic accretion shocks, for a concordance cosmology. We calculate how the shock-processed accretion power and mass current are distributed among different shock Mach numbers, and how they evolve with cosmic time. We calculate the cumulative energy input of cosmic accretion shocks of any Mach number to the intergalactic medium as a function of redshift, and we compare it with the energy output of supernova explosions as well as with the energy input required to reionize the universe. In addition, we investigate and quantify the effect of environmental factors, such as local clustering properties and filament preheating on the statistical properties of these shocks. We find that the energy processed by accretion shocks is higher than the supernova energy output for z<3 and that it becomes more than an order of magnitude higher in the local universe. The energy processed by accretion shocks alone becomes comparable to the energy required to reionize the universe by z~3.5. Finally, we establish both qualitative and quantitatively that both local clustering as well as filament compression and preheating are important factors in determining the statistical properties of the cosmic accretion shock population.Comment: 13 pages, 5 figures, emulateap

Distribution of the very first PopIII stars and their relation to bright z~6 quasars

We discuss the link between dark matter halos hosting the first PopIII stars and the rare, massive, halos that are generally considered to host bright quasars at high redshift z~6. The main question that we intend to answer is whether the super-massive black holes powering these QSOs grew out from the seeds planted by the first intermediate massive black holes created in the universe. This question involves a dynamical range of 10^13 in mass and we address it by combining N-body simulations of structure formation to identify the most massive halos at z~6 with a Monte Carlo method based on linear theory to obtain the location and formation times of the first light halos within the whole simulation box. We show that the descendants of the first ~10^6 Msun virialized halos do not, on average, end up in the most massive halos at z~6, but rather live in a large variety of environments. The oldest PopIII progenitors of the most massive halos at z~6, form instead from density peaks that are on average one and a half standard deviations more common than the first PopIII star formed in the volume occupied by one bright high-z QSO. The intermediate mass black hole seeds planted by the very first PopIII stars at z>40 can easily grow to masses m_BH>10^9.5 Msun by z=6 assuming Eddington accretion with radiative efficiency \epsilon~0.1. Quenching of the black hole accretion is therefore crucial to avoid an overabundance of supermassive black holes at lower redshift. This can be obtained if the mass accretion is limited to a fraction \eta~6*10^{-3} of the total baryon mass of the halo hosting the black hole. The resulting high end slope of the black hole mass function at z=6 is \alpha ~ -3.7, a value within the 1\sigma error bar for the bright end slope of the observed quasar luminosity function at z=6.Comment: 30 pages, 9 figures, ApJ accepte

Multiparameter Riesz Commutators

It is shown that product BMO of Chang and Fefferman, defined on the product of Euclidean spaces can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of Coifman, Rochberg, and Weiss, and at the same time extends the work of Lacey and Ferguson and Lacey and Terwilleger on multiparameter commutators with Hilbert transforms. The method of proof requires the real-variable methods throughout, which is new in the multi-parameter context.Comment: 38 Pages. References updated. To appear in American J Mat

Development of anion-selective membranes

Methods were studied of preparing anion-exchange membranes that would have low resistance, high selectivity, and physical and chemical stability when used in acidic media in a redox energy storage system. Of the twelve systems selected for study, only the system that was based on crosslinked poly-4-vinylpyridinium chloride produced physically strong membranes when equilibrated in l M HCl. The resistivity of the best membrane was 12 ohm-cm, and the transference number for chloride ions was 0.81

Commutators in the Two-Weight Setting

Let $R$ be the vector of Riesz transforms on $\mathbb{R}^n$, and let $\mu,\lambda \in A_p$ be two weights on $\mathbb{R}^n$, $1 < p < \infty$. The two-weight norm inequality for the commutator $[b, R] : L^p(\mathbb{R}^n;\mu) \to L^p(\mathbb{R}^n;\lambda)$ is shown to be equivalent to the function $b$ being in a BMO space adapted to $\mu$ and $\lambda$. This is a common extension of a result of Coifman-Rochberg-Weiss in the case of both $\lambda$ and $\mu$ being Lebesgue measure, and Bloom in the case of dimension one.Comment: v3: suggestions from two referees incorporate

Large-Scale Structure Shocks at Low and High Redshifts

Cosmological simulations show that, at the present time, a substantial fraction of the gas in the intergalactic medium (IGM) has been shock-heated to T>10^5 K. Here we develop an analytic model to describe the fraction of shocked, moderately overdense gas in the IGM. The model is an extension of the Press & Schechter (1974) description for the mass function of halos: we assume that large-scale structure shocks occur at a fixed overdensity during nonlinear collapse. This in turn allows us to compute the fraction of gas at a given redshift that has been shock-heated to a specified temperature. We show that, if strong shocks occur at turnaround, our model provides a reasonable description of the temperature distribution seen in cosmological simulations at z~0, although it does overestimate the importance of weak shocks. We then apply our model to shocks at high redshifts. We show that, before reionization, the thermal energy of the IGM is dominated by large-scale structure shocks (rather than virialized objects). These shocks can have a variety of effects, including stripping ~10% of the gas from dark matter minihalos, accelerating cosmic rays, and creating a diffuse radiation background from inverse Compton and cooling radiation. This radiation background develops before the first stars form and could have measurable effects on molecular hydrogen formation and the spin temperature of the 21 cm transition of neutral hydrogen. Finally, we show that shock-heating will also be directly detectable by redshifted 21 cm measurements of the neutral IGM in the young universe.Comment: 12 pages, 8 figures, submitted to Ap

The Static Dielectric Constant of a Colloidal Suspension

We derive an expression for the static dielectric constant of the colloidal susp ensions based on the electrokinetic equations. The analysis assumes that the ions have the same diffusivity, and that the double layer is much thinner than the radius of curvature of the particles. It is shown that the dielectric increment of the double layer polarization mechanism is originated from the free energy stored in the salt concentration inhomogeniety. We also show that the dominant polarization charges in the theory are at the electrodes, rather than close to the particles.Comment: 15 pages, 1 figur

Triggering the Formation of Halo Globular Clusters with Galaxy Outflows

We investigate the interactions of high-redshift galaxy outflows with low-mass virialized (Tvir < 10,000K) clouds of primordial composition. While atomic cooling allows star formation in larger primordial objects, such "minihalos" are generally unable to form stars by themselves. However, the large population of high-redshift starburst galaxies may have induced widespread star formation in these objects, via shocks that caused intense cooling both through nonequilibrium H2 formation and metal-line emission. Using a simple analytic model, we show that the resulting star clusters naturally reproduce three key features of the observed population of halo globular clusters (GCs). First, the 10,000 K maximum virial temperature corresponds to the ~ 10^6 solar mass upper limit on the stellar mass of GCs. Secondly, the momentum imparted in such interactions is sufficient to strip the gas from its associated dark matter halo, explaining why GCs do not reside in dark matter potential wells. Finally, the mixing of ejected metals into the primordial gas is able to explain the ~ 0.1 dex homogeneity of stellar metallicities within a given GC, while at the same time allowing for a large spread in metallicity between different clusters. To study this possibility in detail, we use a simple 1D numerical model of turbulence transport to simulate mixing in cloud-outflow interactions. We find that as the shock shears across the side of the cloud, Kelvin-Helmholtz instabilities arise, which cause mixing of enriched material into > 20% of the cloud. Such estimates ignore the likely presence of large-scale vortices, however, which would further enhance turbulence generation. Thus quantitative mixing predictions must await more detailed numerical studies.Comment: 21 pages, 11 figures, Apj in pres

Flavor ordering of elliptic flows at high transverse momentum

Based on the quark coalescence model for the parton-to-hadron phase transition in ultra-relativistic heavy ion collisions, we relate the elliptic flow ($v_2$) of high \pt hadrons to that of high \pt quarks. For high \pt hadrons produced from an isospin symmetric and quark-antiquark symmetric partonic matter, magnitudes of their elliptic flows follow a flavor ordering as $(v_{2,\pi}=v_{2,N}) > (v_{2,\Lambda}=v_{2,\Sigma}) > v_{2,K} > v_{2,\Xi} > (v_{2,\phi}=v_{2,\Omega})$ if strange quarks have a smaller elliptic flow than light quarks. The elliptic flows of high \pt hadrons further follow a simple quark counting rule if strange quarks and light quarks have same high \pt spectrum and coalescence probability.Comment: 4 pages, 1 figure, revte